Self-similarity of the statistics in the critical region of Bose condensation of ideal gas in mesoscopic traps: Canonical and grand canonical ensembles

Abstract

For an ideal Bose gas confined in a trap of arbitrary dimension and shape, the features of probabilistic distributions of the number of particles at the ground and all excited levels are studied within canonical and grand canonical ensembles. It is shown that in the critical range of system parameters the statistics is self-similar, and its characteristic scales (mathematical expectation, variance, etc.) are independent of an ensemble used in the description. At the same time, the selfsimilar distributions themselves differ for different ensembles.